An electric power distribution system generally consists of a set of distribution substations, feeders, switches (circuit breakers, reclosers, etc.) electrical loads, and monitoring and control devices. A distribution system delivers electricity from distribution substations via feeders and switches to electrical loads (customers) that connect to feeders. Feeders in a distribution system are usually configured in a radial type to ensure that each load is supplied by only one distribution substation (source) via one feeder at any instant. To maintain the radial configuration, each feeder is linked by normally open (NO) tie-switches to neighboring feeders. The feeder section that is relatively near/far to its source is referred to as upstream/downstream section, while comparing to the feeder section that is relatively far/near to its source. One or more switches in the distribution system may have an associated intelligent electronic device (IED) that has the following monitoring and control functions: (1) measuring and recording electrical and other types of switch related quantities, such as voltage, current, reclosing times (2) monitoring the switch status, (3) operating the switch between open or close, and (4) communicating information to one or more master devices.
Distribution system reliability can be greatly improved by automating feeder operations such as fault detection, isolation, and load restoration. In such systems, IEDs associated with switches monitor the distribution system and communicate the corresponding information to the feeder automation master controllers located in substations. If a fault occurs in the distribution system, the master controller identifies the fault location, generates fault isolation and service restoration solutions in terms of a sequence of switch operations, and sends switching commands to IEDs to control corresponding switches.
An example distribution network is shown in FIG. 1, in a normal operation mode wherein loads are omitted for simplicity, sources (S1 to S7) are oval shaped, NO switches (5, 10, 13, 16, 19, 24, 29) are square shaped, with a diagonal hatch pattern, and normally closed (NC) switches (other numbers) are square shaped, with a vertical hatch pattern. If a fault occurs between switch 1 and 2, the protection function of switch 1 causes switch 1 to open, thereby causing the dashed line circled area to lose power. The boundary switches of the faulted portion of the distribution network include switch 1 and 2. Switch 2 is immediately downstream of the faulted section and thus, is the isolation switch. With reference to FIG. 2, when switches 1 and 2 are open, the faulted portion is isolated and a remaining unserved area is bound by isolation switch 2 and NO switches 5 and 16.
Switches 5 and 16 are referred to as first layer (Layer 1) restoration switches. If the sources, in this case S4 and S7, respectively, can provide the power to the area that is left unserved due to fault isolatin, a first layer restoration solution is possible. If the first layer sources are not capable of providing power to the unserved area, second or even third layer solutions must be performed to provide power to the unserved area. For example, the power sources for layer 2 are S2 and S5. The power sources for a third layer solution are S3 and S6. As should be evident, the second and third layer restoration switches are topologically more “distant” than the first layer restoration switches.
The process to obtain a restoration solution beyond layer 1 is called multi-layer (or multiple-layer) restoration service analysis (RSA). This is sometimes also referred to as a multi-tier service restoration problem, which may be classified as one type of network reconfiguration problems. Due to the potentially large number of switches involved in a multi-layer restoration solution, the process to obtain such solution is generally more challenging than a single-layer solution. With any network reconfiguration problem it is desirable to achieve: computational efficiency, avoiding network violations, minimized switching operations and radiality of the restored network topology.
Network reconfiguration problems may also seek to reduce the overall system loss and relieve overloading conditions in the network. Therefore, a network reconfiguration problem may either be formulated as a loss reduction optimization problem or a load balancing optimization problem. Under normal system operation conditions, network configuration allows the periodical transfer of load from heavily loaded portions of the distribution network to relatively lightly loaded ones, and thus takes advantage of the large degree of load diversity that exists in many distribution systems. Under abnormal system operation conditions, such as planned or forced system outages, the network reconfiguration problem becomes a service restoration problem, which is a special load balancing problem, where the main objective is to restore as many out-of-service loads as possible, without violating system operating and engineering constraints.
As with any other type of network reconfiguration problem, service restoration is a highly complex combinatorial, non-differential, and constrained optimization problem, due to the high number of switching elements in a distribution network, and the non-linear characteristics of the constraints used to model the electrical behavior of the system.
There is therefore a need in the art for a restoration switching analysis method that properly accounts for a greater number of variables and efficiently processes multiple-layer RSA solutions.